# Fluorescence diffusion physics problem

## Homework Statement

As a simple model, suppose you arrange for the intense bleaching pulse of light to illuminate
a cell in a pattern of parallel planes. That is, immediately after bleaching (at time t=0), the
remaining fluorescence intensity Θ(x) has the form Θ(x)= C(i) + C(1)sin(2pix/L) where the two C terms are constants with C(0) greater than C(1). The constant L is the periodicity of the bleach pattern. A. Show that the mean fluorescence intensity immediately after bleaching equals C(0). B. At later times, the fluorescence intensity has the form Θ(x)= C(0) + Δ(t)sin(2pix/L). Derive an expression for the diffusion constant D of the fluorescent molecules in terms of the measured quantity Δ(t). Assume that the region of interest is sufficiently small that you can approximate the cell as having infinite volume.

## Homework Equations

1D diffusion equation perhaps?

## The Attempt at a Solution

obeys the 1D diffusion equation as the instructor told us this.
We only need to calculate within 1 period, from 0 to L.